An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is # 16 #, the cap's height is #2 #, and the cap's radius is #5 #. What is the object's volume?

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Answer 1 · 2018-08-04T13:24:51

1097.37 cu. I would review my answer and improve and make corrections, if any. Please do not edit this answer.

From the dimensions of the spherical cap, the semi-angle that it

subtends at the center of its sphere,

#alpha# rad #= arcsin (4/5) = 0.9273#,

The side length

of the square top of the prism is 2 (4 ) = 8.

The entire volume = Volume of the cap + volume of the prism

= (( volume of the cone + volume of the

spherical cap ) - volume of the cone) + volume of the prism

#= ( 4/3 (5^3)alpha sin alpha - 1/3 pi (4^2)(3)) + (16)(8^2#)

#= 4/3(5^3) ( 0.9273)( 4/5 ) - 1/3 (3.1416)(9)(3)#

#= 1097.37 cu